A cold storage building can also mean it will also double as a combination meat cooler / root cellar if you garden or hunt at all.
Complete temperature stability is reached about 10 feet (3 m) deep so an underground or sub terrain building is going to serve more purposes. (nice cool place to go to on a hot day too
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This is from BC and is banked and not really underground, but the building could be put undergound instead of just banked.
http://www.agf.gov.bc.ca/resmgmt/pub...Veg/331-50.pdf
Wood is more desirable for a structure that is going to be used for vegetable and fruit storage because metal structures can get much colder. If you have your own trees/logs that would be a cheap way of building.
If no veggies or meat are in the plan I would stay above ground.
I saw a Prairie Farm Report show that had a guy in Sask. that built his storage building out of flax straw big square bales and put on a trussed insulated roof. He also made a huge shop from bales. Straw bales can be pretty cheap some years. Lots of info online about straw building.